document.write( "Question 1023150: In the diagram below, BPCR is a rhombus, P is (0,6), C is (6,t) and B is (2,0). The Line PR and BC bisect at Q, PR = 2BC and PR =8sqrt 2\r
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Algebra.Com's Answer #638724 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "From just this information.\r\n" );
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document.write( "BPCR is a rhombus, P is (0,6), C is (6,t) and B is (2,0).\r\n" );
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document.write( "we know that C(6,t) is somewhere on the vertical line whose\r\n" );
document.write( "equation is x=6 (the green line.\r\n" );
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document.write( "we know that since it is a rhombus, PC must equal\r\n" );
document.write( "PC, so we can draw side BP, take a compass and swing an arc like\r\n" );
document.write( "this red one with radius BP, and find only two possibilities\r\n" );
document.write( "for point C, th points where the arc cuts the green line:\r\n" );
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document.write( "So the rhombus is one of these two:\r\n" );
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document.write( "Since we are told that PR = 2BC, we know it must be the second one,\r\n" );
document.write( "not the first.\r\n" );
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document.write( "Since all the sides of a rhombus are equal in\r\n" );
document.write( "length, we use the distance formula to find BP:\r\n" );
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document.write( "\"d=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\r\n" );
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document.write( "We use the distance formula again to set the\r\n" );
document.write( "BP = PC =  √40\r\n" );
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document.write( "\"sqrt%2840%29=sqrt%28%28t-6%29%5E2%2B%286-0%29%5E2%29\"\r\n" );
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document.write( "\"sqrt%2840%29=sqrt%28%28t-6%29%5E2%2B36%29\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"40=%28t-6%29%5E2%2B36\"\r\n" );
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document.write( "\"4=%28t-6%29%5E2\"\r\n" );
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document.write( "take square roots of both sides:\r\n" );
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document.write( "\"%22%22+%2B-+2=t-6\"\r\n" );
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document.write( "\"6+%2B-+2=t\"\r\n" );
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document.write( "So t=4 or 8.  Obviously the answer we \r\n" );
document.write( "want is  C(6,4),\r\n" );
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document.write( "So t=4\r\n" );
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document.write( "We can get the coordinates of R just by\r\n" );
document.write( "counting units.  We know that B is 6\r\n" );
document.write( "units down and 2 units right from P.\r\n" );
document.write( "So R must be 6 units down and 2 units\r\n" );
document.write( "right from C.  That would give us R(8,-2).\r\n" );
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document.write( "We could also get the coordinates of R \r\n" );
document.write( "this way.  We know that C is 6\r\n" );
document.write( "units right and 2 units down from P.\r\n" );
document.write( "So R must be 6 units right and 2 units\r\n" );
document.write( "down from B.  That would also give us \r\n" );
document.write( "R(8,-2).\r\n" );
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document.write( "If we like can check to make sure that \r\n" );
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document.write( "PR = 2BC and PR =8sqrt 2\r\n" );
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document.write( "by using the distance formula, but\r\n" );
document.write( "that's obvious if this is a legitimate\r\n" );
document.write( "problem.\r\n" );
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document.write( "To find the equation of PR, the blue line below:\r\n" );
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document.write( "To find the equation of the PR, the blue line, we use \r\n" );
document.write( "the slope formula to find the slope:\r\n" );
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document.write( "Slope formula:\r\n" );
document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\"\r\n" );
document.write( "where \r\n" );
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document.write( "P(x1,y1) = P(0,6)\r\n" );
document.write( "and where R(x2,y2) = R(8,-2)\r\n" );
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document.write( "m = \"%28%28-2%29-%286%29%29%2F%28%288%29-%280%29%29\"\r\n" );
document.write( "m = \"%28-8%29%2F%28-8%29\"\r\n" );
document.write( "m = 1\r\n" );
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document.write( "Then we use the point-slope formula:\r\n" );
document.write( "y - y1 = m(x - x1)\r\n" );
document.write( "where (x1,y1) = (0,6)\r\n" );
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document.write( "y - 6 = 1(x - 0)\r\n" );
document.write( "y - 6 = x\r\n" );
document.write( "    y = x + 6\r\n" );
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document.write( "Edwin
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